The Penney’s game with group action. (English) Zbl 1486.00002
Summary: Consider equipping an alphabet \(\mathcal{A}\) with a group action which partitions the set of words into equivalence classes which we call patterns. We answer standard questions for Penney’s game on patterns and show non-transitivity for the game on patterns as the length of the pattern tends to infinity. We also analyze bounds on the pattern-based Conway leading number and expected wait time, and further explore the game under the cyclic and symmetric group actions.
MSC:
| 00A08 | Recreational mathematics |
| 00A07 | Problem books |
| 05A19 | Combinatorial identities, bijective combinatorics |
| 60C05 | Combinatorial probability |
| 68T10 | Pattern recognition, speech recognition |
References:
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